The 60-year-old, who won the second-tier European club competition in 2017 with Manchester United, led Roma to the Europa Conference League title last season.
"My concern isn't marking my place in the Roma history books," Mourinho told Sky Sports.
"It's helping these kids (players) to grow, to achieve important things," he said. "It's also helping the Roma fans who have given me so much since day one. It's an immense joy to get to another final.
"The boys give everything, this game is the result of our work, experience, tactical wisdom and knowing how to stay in matches. It's an incredible team."
Mourinho expressed his gratitude to the Roma fans for their exceptional support throughout the Europa League campaign, while asking for their continued backing as the team prepare to return to Serie A action at home to Salernitana on Monday.
"I don't know if I can ask anything more from the fans, but these boys deserve something special on Monday when we will depart Trigoria (training ground)."
However, Roma captain Lorenzo Pellegrini said all the credit should be directed towards Mourinho for the team's success.
"He's different, he makes you realise the importance of the match. We came here and everyone knew what they had to do," he said.
"We study, we organise ourselves, we watch videos. Especially in Europe, you can see what the coach brings us. Mourinho is the creator of this personality of ours."